Supported by the

The

Northwest Probability Seminars are mini-conferences held at the University of Washington and/or Microsoft Research and organized in collaboration with the Oregon State University, the University of British Columbia and the University of Oregon. There is no registration fee.

The Scientific Committee for the NW Probability Seminar 2015 consists of Omer Angel (U British Columbia), Chris Burdzy (U Washington), Zhenqing Chen (U Washington), Yevgeniy Kovchegov (Oregon State U), David Levin (U Oregon), Yuval Peres (Microsoft) and David Wilson (Microsoft).

If you plan to attend, please let us know so that we can plan for food and make name tags.

HOTEL INFORMATION

**
Hotels
near the University of Washington**.

The talks will take place in Savery Hall 264.
See the **map**
the location of Savery Hall and
Padelford Hall (the Department of Mathematics is in the Padelford Hall).
More **
campus maps** are available at the UW Web site.

Parking on UW campus is free on Saturdays only after noon.
See
**
parking information**.

- 10:00
**Coffee**Savery 162 - 11:10 - 11:50
**Mathav Murugan**, University of British Columbia**Anomalous random walks with heavy-tailed jumps**

Sub-Gaussian estimates for the nearest neighbor random walk are typical of fractal-like graphs. In this talk, I will describe a threshold behavior of heavy-tailed random walks on such graphs. This behavior generalizes the classical threshold corresponding to the second moment condition. This talk is based on joint work with Laurent Saloff-Coste. - 12:00 - 12:40
**Zhenan Wang**, University of Washington**Stochastic De Giorgi Iteration**

We will start on the classical De Giorgi iteration for parabolic PDEs. We will explain how a stochastic version of De Giorgi iteration can be developed and applied to prove H\"older continuity for solution of stochastic partial differential equations with measurable coefficient. We will also introduce fine properties for the solutions obtained by applying the stochastic De Giorgi iterations. - 12:50 - 2:20
**Lunch**, catered, Cascade Room in**Haggett Hall**, probability demos and open problems - 2:30 - 3:25
**Balint Virag**, University of Toronto**"Birnbaum Lecture": Dyson's spike and spectral measure of groups**

Consider the graph of the integers with independent random edge weights. In 1953 Dyson showed that for exactly solvable cases even a small amount of randomness results in a logarithmic spike in the spectral measure. With Marcin Kotowski, we prove that this phenomenon holds in great generality. Our result also disproves the lattice case of the Luck and Lott conjecture. - 3:35 - 4:15
**Juan M. Restrepo**, Oregon State University**Defining a Trend of a Multi-Scale Time Series**

Defining a trend for a time series is a fundamental task in time series analyses. It has very practical outcomes: determining a trend in a financial signal, the average behavior of a dynamic process, defining exceptional and likely behavior as evidenced by a time series.On signals and time series that have an underlying stationary statistical distribution there are a variety of ways to estimate a trend, many of which come equipped with a very concrete notion of optimality. Signals that are not statistically stationary are commonly encountered in nature, business, and the social sciences and for these the challenge of defining a trend is two-fold: computing it, and figuring out what this trend means.

Adaptive filtering is frequently explored as a means to calculating/proposing a trend. The Empirical Mode Decomposition and the Intrinsic Time Decomposition are such schemes. I will describe a practical notion of trend based upon the ITD we call a "tendency." We will briefly describe how to compute the tendency and explain its meaning.

- 4:20 - 4:50
**Coffee break**Savery 162 - 4:50 - 5:30
**Yuval Peres**, Microsoft Research**Random walk on the random graph**

I will discuss the behavior of the random walk on two random graph models: on one hand the random regular graph with constant degree, and on the other hand the giant component of the supercritical Erdos-Renyi random graph with constant average degree. In the former case it is known that the walk mixes in logarithmic time and exhibits the cutoff phenomenon. In the latter case, while starting from the worst initial state delays mixing and precludes cutoff, it turns out that starting from a typical vertex induces the rapid mixing behavior of the regular case. (Joint work with Nathanael Berestycki, Eyal Lubetzky and Allan Sly.) - 6:15 No-host
**dinner**.- Restaurant:
**Chiang's Gourmet**. 7845 Lake City Way NE, Seattle, WA 98115, Tel: (206) 527-8888 -
**Menu** - Google
**directions**with map - Google
**directions**with close-up map of restaurant neighborhood - You cannot enter the restaurant from Lake City Way driving north (you can if you are driving south). Turn left from Lake City Way into NE 80-th St and then turn left into the restaurant parking lot.
- Google
**photo**of the restaurant looking from Lake City Way - Google
**photo**of the restaurant looking from NE 80-th St

- Restaurant: